Your disk device nomenclature will definitely change. As far as the OS all you have to do is make a copy, by whatever means you feel the need to use. I would not destroy the old device until you have fully tested the target device/s.

Yes one you present the LUNS on the CX3-40F new device files will be generated but that's okay. Use LV Mirroring to mirror to your new LUNS and then Unmirror the EMC Disks. This is what I mean
The best way to proceed to is have a fiber cable from the CX3-40F passed to your server. Hopefully you have a free fiber port available. Here is an example if you have /dev/vg01 with 5 LUNS on the EMC, then preset to your server 5 LUNS from the CX3-40F. Add those 5 LUNs to your /dev/vg01, then perform a lvextend -m 2 /dev/vg01/lvFirst NewLUNDevice. Once you have mirrored all your Logical Volumes on VG01 onto your new LUNS. Then your are ready to do the LVREMOVE of your EMS disks. You can do the LVREMOVE anytime your wish or are satisfied that you have successfully mirrored your data. There is no downtime of application and the move will be transparent to your application.

I'm imagine I'm late with this response, but are you physically moving the SAN to a new site? Or just the disks perhaps? If so, do a vgexport -s -m mapfile /dev/vgxxx before you disconnect the device. Of course make a backup first. Save the mapfile to your PC or something. When you connect the SAN to the new machine it will build new device files. You will have to recreate a new volume group with the mknod command, then using the mapfile do a vgimport. The volume group will be on the new machine along with all the data.